Near-to-planar three-jet events at NNLL accuracy

Abstract

We extend the ARES method for next-to-next-to-leading-logarithmic (NNLL) QCD resummations to three-jet event shapes in $e^{+}{e}^{-}$ collisions in the near-to-planar limit. In particular, we define a NNLL radiator for three hard emitters, and discuss new features of NNLL corrections arising specifically in this case. As an example, we present predictions for the $D$-parameter, matched to exact NLO. After inclusion of hadronisation corrections in the dispersive approach, we compare our predictions with LEP1 data.

Comments: 47 pages, 9 figures. Added references and amended acknowledgements